Scala analysis: xen18-ayers-table-47
Reciprocals of Golden Mean in Octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 175.078 cents 175.078000 2: 283.282 cents 283.282000 3: 458.359 cents 458.359000 4: 741.641 cents 741.641000 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 458.3590 cents 458.3590 1: 175.0780 cents 175.0780 2: 108.2040 cents 108.2040 3: 175.0770 cents 175.0770 4: 283.2820 cents 283.2820 5: 458.3590 cents 458.3590
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 108.20400 cents 1: 1 175.07700 cents 1: 1 175.07800 cents 1: 1 283.28200 cents 1: 1 458.35900 cents 2: 1 283.28100 cents 2: 1 283.28200 cents 2: 1 458.35900 cents 2: 1 633.43700 cents 2: 1 741.64100 cents 3: 1 458.35900 cents 3: 1 566.56300 cents 3: 1 741.64100 cents 3: 1 916.71800 cents 3: 1 916.71900 cents 4: 1 741.64100 cents 4: 1 916.71800 cents 4: 1 1024.92200 cents 4: 1 1024.92300 cents 4: 1 1091.79600 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 175.1 283.3 458.4 741.6 1200.0 175.1 : 108.2 283.3 566.6 1024.9 1200.0 283.3 : 175.1 458.4 916.7 1091.8 1200.0 458.4 : 283.3 741.6 916.7 1024.9 1200.0 741.6 : 458.4 633.4 741.6 916.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 108.2040 .. 458.3590 cents 350.15500 cents 108.20400 cents 2: 283.2810 .. 741.6410 cents 458.36000 cents -175.07800 cents 3: 458.3590 .. 916.7190 cents 458.36000 cents -283.28200 cents 4: 741.6410 .. 1091.7960 cents 350.15500 cents -175.07800 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 108.20400 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 458.35900 cents Average / Smallest step : 2.218033 Largest / Average step : 1.909829 Largest / Smallest step : 4.236063 Median interval of one step : 175.07800 cents, amount: 1 Least squares average step : 201.51424 cents, oct.: 1007.57118 cents Scale is not proper Scale is a mode of a 610-tone equal temperament with octave 1200.000 cents degrees: 89 144 233 377 610 Least number of segments generator : 307 of 603.934 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 377 of 741.639 cents and inv. generated superset size: 6 = 1 more = 120.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDE Step pattern size order : CABDE Scale is not a Constant Structure Scale diversity : 1.426513 Lumma stability : 0.180340 Lumma impropriety factor : 0.527865 Rothenberg efficiency : 0.540000 redundancy: 0.460000 Efficiency x scale size : 2.700000 Number of different interval sizes : 14 = 3.50000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00100 cents Most common intervals : 458.35900 cents & inv., amount: 3 Most common triad is 0.0 458.359 741.641 cents, amount: 2 Number of recognisable fifths : 0 Formal octave complements present : 3 = 60.0000% -- Rational properties --
FIT/MODE
5: 1 0 1 1 2 N T3 SD: 37.4830 c. M:-64.9220 c. 7: 1 1 1 1 3 N M DE S SD: 44.3128 c. M:-59.5751 c. 8: 1 1 1 2 3 N SD: 14.4786 c. M: 25.0780 c. 13: 2 1 2 3 5 N SD: 5.5066 c. M:-9.5374 c. 21: 3 2 3 5 8 N SD: 2.1068 c. M: 3.6494 c. 34: 5 3 5 8 13 N SD: 0.8042 c. M:-1.3926 c. 55: 8 5 8 13 21 N SD: 0.3072 c. M: 0.5325 c. 89: 13 8 13 21 34 N SD: 0.1174 c. M:-0.2029 c. 144: 21 13 21 34 55 N SD: 0.0448 c. M: 0.0780 c. 233: 34 21 34 55 89 N SD: 0.0171 c. M:-0.0293 c. 377: 55 34 55 89 144 N SD: 0.0065 c. M: 0.0117 c. 610: 89 55 89 144 233 N SD: 0.0025 c. M:-0.0040 c. 987: 144 89 144 233 377 N SD: 0.0010 c. M: 0.0020 c. 1597: 233 144 233 377 610 N SD: 0.0005 c. M: 0.0008 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x x 3:4 S SD: 19.8430 cents 3 x x 4:5:6 S SD: 49.3776 cents 4 x x 5:6:8 S SD: 27.4176 cents 5 x 6:7:8:10 S SD: 36.7863 cents 6 x 7:8:9:12 S SD: 14.6187 cents 7 x 8:9:11:14 SD: 17.5459 cents 8:9 x 10:12:16 S SD: 21.7899 cents 9:10:11:12:14:18 SD: 15.8524 cents 10:11:12:13:15:20 SD: 10.4705 cents 11:12:13:14:17:22 SD: 9.8898 cents 16:18:19:21:25:32 SD: 9.2699 cents 17:19:20:22:26:34 SD: 4.4271 cents 30:33:35:39:46:60 SD: 3.9530 cents 37:41:44:48:57:74 SD: 3.9378 cents 39:43:46:51:60:78 SD: 1.9680 cents 56:62:66:73:86:112 SD: 0.4053 cents 198:219:233:258:304:396 SD: 0.3437 cents 208:230:245:271:319:416 SD: 0.3333 cents 254:281:299:331:390:508 SD: 0.2357 cents 264:292:311:344:405:528 SD: 0.2073 cents 310:343:365:404:476:620 SD: 0.1927 cents 320:354:377:417:491:640 SD: 0.1471 cents 376:416:443:490:577:752 SD: 0.1321 cents 518:573:610:675:795:1036 SD: 0.0917 cents 574:635:676:748:881:1148 SD: 0.0536 cents